Gaussian approximation (GA) is widely used to construct polar codes. However when the code length is long, the subchannel selection inaccuracy due to the calculation error of conventional approximate GA (AGA), which uses a two-segment approximation function, results in a catastrophic performance loss. In this paper, new principles to design the GA approximation functions for polar codes are pro...

This paper presents a definition of a construction for long polar codes. Recently, we know that partial order is a universal property of the construction with a sublinear complexity for polar codes. In order to describe the partial order, addition and left-swap operators are only defined as universal up to now. In this study, we first propose 1 + log2 log2 N universal operators to describe mult...

Reed-Solomon and BCH codes were considered as kernels of polar codes by Mori and Tanaka in [6] and Korada, Şaşoğlu, and Urbanke in [4] to create polar codes with large exponents. For codes of length l ≤ q, Mori and Tanaka showed Reed-Solomon codes give the best possible exponent, where q is the size of the input alphabet. However, considering larger matrices over Fq yields better exponents for ...

Polarization codes were recently introduced by Arıkan. They achieve the capacity of arbitrary symmetric binaryinput discrete memoryless channels (and even extensions thereof) under a low complexity successive decoding strategy. The original polar code construction is closely related to the recursive construction of Reed-Muller codes and is based on the 2× 2 matrix

Since its invention, polar code has received a lot of attention because of its capacity-achieving performance and low encoding and decoding complexity. Successive cancellation decoding (SCD) and belief propagation decoding (BPD) are two of the most popular approaches for decoding polar codes. SCD is able to achieve good error-correcting performance and is less computationally expensive as compa...

A heuristic construction of polar codes for successive cancellation list (SCL) decoding with a given list size is proposed to balance the trade-off between performance measured in frame error rate (FER) and decoding complexity. Furthermore, a construction based on dynamically frozen bits with constraints among the ”low weight bits” (LWB) is presented. Simulation results show that the LWB-polar ...

Maritime traffic volume in the Arctic is growing for several reasons: climate change is resulting in less ice in extent, duration, and thickness; economic drivers are inducing growth in resource extraction traffic, community size (affecting resupply) and adventure tourism. This dynamic situation, coupled with harsh weather, variable operating conditions, remoteness, and lack of straightforward ...

—In this letter, we propose parallel SC (Successive Cancellation) decoder and parallel SC-List decoder for polar codes. The parallel decoder is composed of) 1 (2   m M m component decoders working in parallel and each component decoder decodes a Polar code of a block size of M / 1 of the original Polar code. Therefore the parallel decoder has M times faster decoding speed. Our simulation resu...